Question: Solve for $x$ and $y$ using elimination. ${2x+3y = 30}$ ${-2x+4y = -2}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $7y = 28$ $\dfrac{7y}{{7}} = \dfrac{28}{{7}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {2x+3y = 30}\thinspace$ to find $x$ ${2x + 3}{(4)}{= 30}$ $2x+12 = 30$ $2x+12{-12} = 30{-12}$ $2x = 18$ $\dfrac{2x}{{2}} = \dfrac{18}{{2}}$ ${x = 9}$ You can also plug ${y = 4}$ into $\thinspace {-2x+4y = -2}\thinspace$ and get the same answer for $x$ : ${-2x + 4}{(4)}{= -2}$ ${x = 9}$